cyk

std.seq.cyk · Level L3

Whether a grammar in Chomsky normal form derives a word, as 1 or 0, by the CYK recognizer, and the table X[A, i, j] of which nonterminals derive which parts w[i:j]. The grammar is k nonterminals, terminal rules Tm[A, σ] for A → σ, binary rules A → B C listed as RA, RB, RC, and a start symbol. The table is closed under the binary rules by L steps of cyk_step, each one batched product per rule. A word of length L ≥ 1; CYK decides membership, unlike a bounded search, whose failure would prove nothing.

S ⇒* w ⇔ X[S, 0, L] = 1

Signature

cyk(Tm: f64[k, s], RA: i64[q], RB: i64[q], RC: i64[q], start: i64[], word: i64[L]) → f64[], f64[k, L+1, L+1]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference the textbook CYK table by span length, in Python in exact rational arithmetic, on all 40 test cases.
All 3,534 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

cyk_step

Called by

—

sha256:0e0a4e7669f1a6ec91d73937351b3e4f5f0156276922ffb61d0611a7db2ef6f1

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.seq.cyk · Ω:cyk
Pins: sha256:6a71d62c34befc41064219e0decc3f46bed769536c556184305084656aa7ce62this graph and the 1 it reaches through calls
Evidence: sha256:8c4b93594a2a665445fa4e5cc131daadb2c42d4550a9588364b3ccdde37722bcthe hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.